3,465 results on '"Jinde Cao"'
Search Results
2. A review on epidemic models in sight of fractional calculus
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Kottakkaran Sooppy Nisar, Muhammad Farman, Mahmoud Abdel-Aty, and Jinde Cao
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Epidemic model ,Fractional calculus ,Stability ,Integral operator ,Mittag–Leffler kernel ,Power law ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
Biomathematics has become one of the most significant areas of research as a result of interdisciplinary study. Chronic diseases sometimes referred to as non-communicable and communicable diseases, are conditions that develop over an extended period as a result of different factors like genetics, lifestyle, and environment. The most important common types of disease are cardiovascular, alcohol, cancer, and diabetes. More than three-quarters of the world’s (31.4 million) deaths occur in low- and middle-income nations, which are disproportionately affected by different infections. Fractional Calculus is a prominent topic for research within the discipline of Applied Mathematics due to its usefulness in solving problems in many different branches of science, engineering, and medicine. Recent researchers have identified the importance of mathematical tools in various disease models as being very useful to study the dynamics with the help of fractional and integer calculus modeling. Due to the complexity of the underlying connections, both deterministic and stochastic epidemiological models are founded on an inadequate understanding of the infectious network. Over the past several years, the use of different fractional operators to model the problem has grown, and it is now a common way to study how epidemics spread. Recently, researchers have actively considered fractional calculus to study different diseases like COVID-19, cancer, TB, HIV, dengue fever, diabetes, cholera, pine welts, smoking and heart attacks, etc. With the help of fractional operator, we modified a mathematical model for the dynamical transmission, analysis, treatment, vaccination, and precaution leveling necessary to mitigate the negative impact of illness on society in the long run, overcoming the memory effect without defining or considering others parameters. In this review paper, we considered all the recent studies based on the fractional modeling of infectious and non-infectious diseases with different fractional operators such as Caputo, Caputo Fabrizio, ABC, and constant proportional with Caputo, etc. This review paper aims to bring all the information together by considering different fractional operators and their uses in the field of infectious disease modeling. The steps taken to accomplish the goal were developing a mathematical model, identifying the equilibrium point, figuring out the minimal reproductive number, and assessing the stability around the equilibrium point.For future direction, we consider the cancer model to study the growth cells of cancer and the impact of therapy to control infections. An equilibrium solution and an analysis of the behavior dynamics of the cell spread with treatment in the form of chemotherapy were obtained. The simulation shows that the population of cancer cells is influenced by the pace of cancer cell growth with the Caputo fractional derivative. The acquired results show how effective and precise the suggested approach is in helping to better understand how chemotherapy works. Chemotherapy medications have been found to increase immunity against particular cancer by reducing the number of tumor cells. Further, we suggested some future work directions with the help of the new hybrid fractional operator. Our innovative methodology might have significant effects on global stakeholders, policymakers, and national health systems. The current strategies for controlling outbreaks and the vaccination and prevention policies that have been implemented would benefit from a more accurate representation of the dynamics of contagious diseases, which necessitates the development of highly complex mathematical models. Microorganisms, interactions between individuals or groups, and environmental, social, economic, and demographic factors on a broader scale are all examples.
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- 2023
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3. Mean-square consensus of a semi-Markov jump multi-agent system based on event-triggered stochastic sampling
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Duoduo Zhao, Fang Gao, Jinde Cao, Xiaoxin Li, and Xiaoqin Ma
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event-triggered ,stochastic sampling ,lyapunov function ,semi-markovian switching ,multi-agent systems ,mean-square consensus ,Biotechnology ,TP248.13-248.65 ,Mathematics ,QA1-939 - Abstract
This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To effectively reduce communication costs and control updates, we propose an event-triggered protocol based on stochastic sampling. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Using the event-triggered strategy, we present sufficient conditions to ensure mean square consensus. Finally, we provide a numerical example demonstrating the effectiveness of the theoretical results.
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- 2023
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4. GAGCN: Generative adversarial graph convolutional network for non‐homogeneous texture extension synthesis
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Shasha Xie, Wenhua Qian, Rencan Nie, Dan Xu, and Jinde Cao
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attention mechanism ,generative adversarial networks ,graph convolutional networks ,non‐homogeneous texture synthesis ,Photography ,TR1-1050 ,Computer software ,QA76.75-76.765 - Abstract
Abstract In the non‐homogeneous texture synthesis task, the overall visual characteristics should be consistent when extending the local patterns of the exemplar. The existing methods mainly focus on the local visual features of patterns but ignore the relative position features that are important for non‐homogeneous texture synthesis. Although these methods have achieved success on homogeneous textures, they cannot perform well on non‐homogeneous textures. Thus, it is desirable to model the dependence between pixels to improve the synthesis performance. To ensure synthesis results from both the local detail structure and the overall structure, this paper proposes a non‐homogeneous texture extended synthesis model (GAGCN) combining the generate adversarial network (GAN) and the graph convolutional network (GCN). The GAN learns the internal distribution of image patches, which makes the synthetic image have rich local details. The GCN learns the latent dependence between pixels according to the statistical characteristics of the image. Based on this, a novel graph similarity loss is proposed. This loss describes the latent spatial differences between the sample image and the generated image, which helps the model to better capture global features. Experiments show that our method outperforms existing methods on non‐homogeneous textures.
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- 2023
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5. Razumikhin and Krasovskii stability of impulsive stochastic delay systems via uniformly stable function method
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Lijun Pan, Jianqiang Hu, and Jinde Cao
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stochastic delay systems ,Razumikhin ,Krasovskii ,impulse ,uniformly stable function ,Analysis ,QA299.6-433 - Abstract
This paper generalizes Razumikhin-type theorem and Krasovskii stability theorem of impulsive stochastic delay systems. By proposing uniformly stable function (USF) in the form of impulse as a new tool, some properties about USF and some novel pth moment decay theorems are derived. Based on these new theorems, the stability theorems of impulsive stochastic linear delay system are acquired via the Razumikhin method and the Krasovskii method. The obtained results enhance the elasticity of the impulsive gain by comparing the previous results. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results.
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- 2023
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6. Platoon-based collision-free control for connected and automated vehicles at non-signalized intersections
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Jian Gong, Yuan Zhao, and Jinde Cao
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connected automated vehicles ,intersection control ,platoon control ,collision avoidance ,trajectory optimization ,Mathematics ,QA1-939 ,Applied mathematics. Quantitative methods ,T57-57.97 - Abstract
This paper proposes a distributed collision-free control scheme for connected and automated vehicles (CAVs) at a non-signalized intersection. We first divide an intersection area into three sections, i.e., the free zone, the platoon zone, and the control zone. In order to enable the following vehicles to track the trajectory of their leading vehicle in the platoon zone and the control zone, as well as to guarantee the desired distance between any two adjacent vehicles, the distributed platoon controllers are designed. In the control zone, each vehicular platoon is taken as a whole to be coordinated via an intersection coordination unit (ICU). To avoid collision between each pair of the conflicting platoons approaching from different directions, a platoon-based coordination strategy is designed by scheduling the arrival time of each leading vehicle of different platoons. Specially, considering traffic efficiency and fuel economy, the optimal control problem of the leading vehicle is formulated subject to the constraint of allowable minimum arrival time, which is derived from coordination with other approaching platoons. The Pontryagin Minimum Principle (PMP) and phase-plane method are applied to find the optimal control sequences. Numerical simulations show the effectiveness of this scheme.
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- 2023
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7. The rutting model of semi-rigid asphalt pavement based on RIOHTRACK full-scale track
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Bo Kou, Jinde Cao, Wei Huang, and Tao Ma
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semi-rigid asphalt pavement ,rutting depth prediction model ,feature selection ,r-f model ,random forest ,Biotechnology ,TP248.13-248.65 ,Mathematics ,QA1-939 - Abstract
Semi-rigid asphalt pavement has a wide range of application cases and data bases, and rutting is a typical failure mode of semi-rigid asphalt pavement. The establishment of an accurate rutting depth prediction model is of great significance to pavement design and maintenance. However, due to the lack of perfect theoretical system and systematic research data, the existing rutting prediction model of semi-rigid asphalt pavement is not accurate. In this paper, machine learning and mechanical-empirical model are combined to study the feature selection affecting the rutting evolution and rutting depth model of semi-rigid asphalt pavement. First, the particle swarm optimization random forest model is used to select the important features that affect the evolution of rutting depth. Second, the R-F model based on important features is proposed for the first time, which is compared with modification of rutting model in the Chinese Specifications for Design of Highway Asphalt Pavement (JTG D50-2017) and R-B model based on the improved Burgers model. The results show that the R-F model has more accurate prediction ability and better generalization ability, and it does not need complex data preprocessing and noise reduction. Here, the machine learning method is introduced to analyze the data characteristics, and the R-F rutting depth prediction model framework is innovatively proposed, which greatly improves the applicability and accuracy of the existing model framework.
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- 2023
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8. MPEFNet: Multilevel Progressive Enhancement Fusion Network for Pansharpening
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He Li, Rencan Nie, Jinde Cao, Biaojian Jin, and Yao Han
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Convolutional neural network (CNN) ,image fusion ,multilevel ,multispectral (MS) image ,pansharpening ,Ocean engineering ,TC1501-1800 ,Geophysics. Cosmic physics ,QC801-809 - Abstract
Remote sensing image fusion is a key technique to fuse low spatial resolution multispectral (MS) images with high spatial resolution panchromatic (PAN) images to obtain high spatial resolution multispectral images. However, many existing fusion algorithms typically perform a single upsampling on the MS image to match its spatial resolution with that of the PAN image, and subsequently output the fused image through steps of feature extraction, fusion, and decoding. This single-stage fusion approach not only fails to fully utilize the low-frequency and high-frequency spatial information in the PAN image, but also leads to inadequate extraction of internal spatial and spectral information in the original MS image, resulting in problems such as blurring, artifacts, and incomplete spectral information recovery in the fused image. To address these issues, this article proposed a multilevel progressive enhancement fusion network. To fully fuse the spatial and spectral information of different resolution images, this article employs a three-stage network structure. The high preserving block is used to alleviate spatial detail distortion and spectral information loss caused by upsampling. Bands aggregation module and spatial aggregation module are used to refine the feature extraction module's spectral and spatial detail features. Meanwhile, the enhanced fusion module further performs self-enhancement fusion on the refined features, as well as mutual-enhancement fusion with the original information. The method is superior to the comparison method by qualitative analysis and quantitative comparison on the IKONOS and WorldView-2 datasets.
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- 2023
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9. Observer-Based Output Feedback Tracking Consensus for Multi-Agent Systems With Periodic Intermittent Communication and Input Saturation
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Yiping Luo, Beining Bao, and Jinde Cao
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Multi-agent systems ,consensus ,input saturation ,periodic intermittent control ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - Abstract
This paper studies the semi-global tracking consensus problem for general multi-agent networks with input saturation and periodic intermittent communication. The considered problem is solved by proposing an efficient distributed observer-based periodic intermittent control protocol, where the control inputs of follower agents are subjected to saturation. First, a low-gain feedback method is introduced to suppress the input saturation constraint, and the output feedback control protocol for agents are defined based on the algebraic Riccati equation. Next, a state observer is designed to ensure that observer can realize state reconstruction under the condition that the state of agents cannot be measured directly in the process of information interaction. Then, according to the Lyapunov second method and related linear inequalities, the sufficient conditions which are necessary for a state observation system for the coordinated tracking consensus, are defined under the conditions of input saturation and periodic intermittent communication. Finally, a simulation is performed to prove the expectant algorithm.
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- 2023
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10. Optimizing information-driven awareness allocation for controlling activity-triggered epidemic spread
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Jie Chen, Maobin Hu, and Jinde Cao
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co-evolution spreading ,epidemic dynamics ,awareness trade-off ,Science ,Physics ,QC1-999 - Abstract
In the contemporary era, the advent of epidemics instigates a substantial upswing in relevant information dissemination, bolstering individuals’ resistance to infection by concurrently reducing activity contacts and reinforcing personal protective measures. To elucidate this intricate dynamics, we introduce a composite four-layer network model designed to capture the interplay among information-driven awareness, human activity, and epidemic spread, with a focus on the allocation of individuals’ limited attention in diminishing activity frequency and self-infection rates. One intriguing observation from our findings is an anomalous, concave non-monotonic relationship between awareness trade-off and epidemic spread, with a more pronounced prevalence at an intermediate least awareness efficacy. This underscores the inadvisability of relaxing self-protection through reduced activity frequency or compensating for increased activity frequency by enhancing self-protection. Especially noteworthy is the significance of enhancing self-protection in response to heightened information dissemination and inherent activity demands to curtail infection risk. However, in scenarios with increasing ancillary activity frequency, the emphasis should exclusively shift towards reducing activity exposure. The model establishes a theoretical threshold for accurately predicting awareness efficacy in epidemic outbreaks. Optimal awareness allocation consistently resides at the extremes—either completely avoiding unnecessary activity contact or adopting full self-protection. This guidance, contingent on information level and activity demand, offers valuable insights into the delicate balance between individual behaviors and epidemic prevention.
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- 2024
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11. Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse
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Xia Zhou, Chunya Huang, Ping Li, Zhongjun Ma, and Jinde Cao
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Markov jump multi-agent systems ,DAs, DoS attacks ,impulsive control ,identical consensus ,Analysis ,QA299.6-433 - Abstract
The issue of leader-following identical consensus for nonlinear Markov jump multiagent systems (NMJMASs) under deception attacks (DAs) or denial-of-service (DoS) attacks is investigated in this paper. The Bernoulli random variable is introduced to describe whether the controller is injected with false data, that is, whether the systems are subjected to DAs. A connectivity recovery mechanism is constructed to maintain the connection among multi-agents when the systems are subjected to DoS attack. The impulsive control strategy is adopted to ensure that the systems can normally work under DAs or DoS attacks. Based on graph theory, Lyapunov stability theory, and impulsive theory, using the Lyapunov direct method and stochastic analysis method, the sufficient conditions of identical consensus for Markov jump multi-agent systems (MJMASs) under DAs or DoS are obtained, respectively. Finally, the correctness of the results and the effectiveness of the method are verified by two numerical examples.
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- 2023
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12. Prespecified-time bipartite synchronization of coupled reaction-diffusion memristive neural networks with competitive interactions
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Ruoyu Wei and Jinde Cao
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memristor ,reaction-diffusion term ,neural networks ,competitive interactions ,bipartite synchronization ,prespecified-time synchronization ,Biotechnology ,TP248.13-248.65 ,Mathematics ,QA1-939 - Abstract
In this paper, we investigate the prespecified-time bipartite synchronization (PTBS) of coupled reaction-diffusion memristive neural networks (CRDMNNs) with both competitive and cooperative interactions. Two types of bipartite synchronization are considered: leaderless PTBS and leader-following PTBS. With the help of a structural balance condition, the criteria for PTBS for CRDMNNs are derived by designing suitable Lyapunov functionals and novel control protocols. Different from the traditional finite-time or fixed-time synchronization, the settling time obtained in this paper is independent of control gains and initial values, which can be pre-set according to the task requirements. Lastly, numerical simulations are given to verify the obtained results.
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- 2022
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13. Attractivity criterion on a delayed tick population dynamics equation with a reproductive function $ f(u) = ru^{\gamma}e^{-\sigma u} $
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Fawaz E Alsaadi, Chuangxia Huang, Madini O Alassafi, Reem M Alotaibi, Adil M Ahmad, and Jinde Cao
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tick population ,delay ,equilibrium ,attractivity ,Biotechnology ,TP248.13-248.65 ,Mathematics ,QA1-939 - Abstract
The aim of this article is to analyze the delay influence on the attraction for a scalar tick population dynamics equation accompanying two disparate delays. Taking advantage of the fluctuation lemma and some dynamic inequalities, we derive a criterion to assure the persistence and positiveness on the considered model. Furthermore, a time-lag-dependent condition is proposed to insure the global attractivity for the addressed model. Besides, we give some simulation diagrams to substantiate the validity of the theoretical outcomes.
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- 2022
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14. Global dynamics of a dengue fever model incorporating transmission seasonality
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Min Zhu, Tingting Feng, Yong Xu, and Jinde Cao
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dengue fever model ,diffusion-reaction system ,periodicity ,global stability ,Analysis ,QA299.6-433 - Abstract
The changes of seasons cause that the transmission of dengue fever is characterized by periodicity. We develop a dengue fever transmission model incorporating seasonal periodicity and spatial heterogeneity. Based on the well-posedness of solution for this model, we propose its basic reproduction number R0, and we discuss the properties of this number including its limiting form when the diffusion coefficients change. Moreover, the dynamical behavior of this model infers that if R0 ⩽ 1, then the disease-free periodic solution is globally asymptotically stable, and if R0 > 1, then the model possesses a positive periodic solution, which is globally asymptotically stable. These theoretical findings are further illustrated by the final numerical simulations. Additionally, we add that the similar problem has been investigated by M. Zhu and Y. Xu [A time-periodic dengue fever model in a heterogeneous environment, Math. Comput. Simul., 155:115–129, 2019] in which some dynamical results have been studied only on the cases R0 < 1 and R0 > 1. Our results not only include the scenario on the case R0 = 1, but also involve the more succinct conditions on the cases R0 < 1 and R0 > 1.
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- 2023
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15. New results of global Mittag-Leffler synchronization on Caputo fuzzy delayed inertial neural networks
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Xiangnian Yin, Hongmei Zhang, Hai Zhang, Weiwei Zhang, and Jinde Cao
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Caputo derivative ,global Mittag-Leffler synchronization ,fuzzy inertial neural networks ,variable substitution ,Analysis ,QA299.6-433 - Abstract
This article is devoted to discussing the problem of global Mittag-Leffler synchronization (GMLS) for the Caputo-type fractional-order fuzzy delayed inertial neural networks (FOFINNs). First of all, both inertial and fuzzy terms are taken into account in the system. For the sake of reducing the influence caused by the inertia term, the order reduction is achieved by the measure of variable substitution. The introduction of fuzzy terms can evade fuzziness or uncertainty as much as possible. Subsequently, a nonlinear delayed controller is designed to achieve GMLS. Utilizing the inequality techniques, Lyapunov’s direct method for functions and Razumikhin theorem, the criteria for interpreting the GMLS of FOFINNs are established. Particularly, two inferences are presented in two special cases. Additionally, the availability of the acquired results are further confirmed by simulations.
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- 2023
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16. Impulsive Controllers Design for the Practical Stability Analysis of Gene Regulatory Networks with Distributed Delays
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Jinde Cao, Trayan Stamov, Gani Stamov, and Ivanka Stamova
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practical stability ,impulses ,distributed delays ,Lyapunov functions ,Thermodynamics ,QC310.15-319 ,Mathematics ,QA1-939 ,Analysis ,QA299.6-433 - Abstract
This paper studies gene regulatory networks (GRNs) with distributed delays. The essential concept of practical stability of the genes is introduced. We investigate the problems of practical stability and global practical exponential stability of the GRN model under an impulsive control. New practical stability criteria are proposed by designing appropriate impulsive controllers via the Lyapunov functions approach. In the design of the impulsive controller, we consider the effect of impulsive perturbations at fixed times and distributed delays on the stability of the considered GRNs. Several numerical examples are also presented to justify the proposed criteria.
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- 2023
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17. Non-commuting graph of the dihedral group determined by Hosoya parameters
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Muhammad Salman, Tahira Noreen, Masood Ur Rehman, Jinde Cao, and Muhammad Zafar Abbas
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15A27 ,05C07 ,05C12 ,05C92 ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
Hosoya introduced the concept of graph terminologies in chemistry and provide a modeling for molecules. This modeling leads to predict the chemical properties of molecules, easy classification of chemical compounds, computer simulations and computer-assisted design of new chemical compounds. In this article, we determine the non-commuting graph associated with the dihedral group by using three Hosoya parameters (Hosoya polynomial, reciprocal Hosoya polynomial and Hosoya index). These Hosoya parameters contain a pile of information about distance structure as well as the edge independent structure of the above-mentioned graph.
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- 2022
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18. Almost periodic solutions of fuzzy shunting inhibitory CNNs with delays
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Ardak Kashkynbayev, Moldir Koptileuova, Alfarabi Issakhanov, and Jinde Cao
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shunting inhibitory cellular neural networks ,fuzzy logic ,almost periodic function ,delay differential equations ,global stability ,Mathematics ,QA1-939 - Abstract
In the present paper, we prove the existence of unique almost periodic solutions to fuzzy shunting inhibitory cellular neural networks (FSICNN) with several delays. Further, by means of Halanay inequality we analyze the global exponential stability of these solutions and obtain corresponding convergence rate. The results of this paper are new, and they are concluded with numerical simulations confirming them.
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- 2022
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19. Нечетко-логические методы в задаче детектирования границ объектов
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Maksim Bobyr, Alexander Arkhipov, Sergey Gorbachev, Jinde Cao, and Siddhartha Bhattacharyya
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нечёткая логика ,детектор канни ,выделение границ ,оператор собеля ,центр тяжести ,Electronic computers. Computer science ,QA75.5-76.95 - Abstract
Рассматривается задача уменьшения вычислительной сложности методов выделения контуров на изображениях. Решение поставленной задачи достигается модификацией детектора Канни двумя нечетко-логическими методами, позволяющими сократить число проходов по исходному изображению: в-первом случае, путем исключения двух проходов, связанных с определением наличия соседства претендующего на границу пикселя со смежными в рамке размером 3´3, а во-втором случае, исключением операции определения угла направления градиента путем формирования данной величины комбинацией нечетких правил. Целью работы является уменьшение времени детектирования границ объектов на фото- видео-изображениях, за счет уменьшения вычислительной сложности применяемых методов. Интеллектуализация процесса детектирования границ осуществляется частичным повтором вычислительных операций, используемых в детекторе Канни, с дальнейшей заменой наиболее сложных вычислительных процедур. В предлагаемых методах после определения величины градиента и угла его направления осуществляется фаззификация восьми входных переменных, в качестве которых используется разность градиентов между центральной и смежными ячейками в рамке размером 3´3. Затем строится база нечетких правил. В первом методе в зависимости от угла направления градиента используются четыре нечетких правила и исключается один проход. Во втором методе шестнадцать нечетких правил сами задают угол направления градиента, при этом исключается два прохода вдоль изображения. Разность градиентов между центральной ячейкой и смежными ячейками позволяет учитывать форму распределения градиента. Затем на основе метода центра тяжести осуществляется дефаззификация результирующей переменной. Дальнейшее использование нечетких a-срезов позволяет осуществить бинаризацию результирующего изображения с выделением на нем границ объектов. Для оценки вычислительной скорости работы предложенных нечетких методов детектирования границ в среде Microsoft Visual Studio было разработано программное обеспечение. Представленные экспериментальные результаты показали, что уровень шума зависит от величины a-среза и параметров меток трапециевидных функций принадлежности. Ограничением двух методов является использование кусочно-линейных функций принадлежности. Экспериментальные исследования работоспособности предложенных методов детектирования контуров показали, что время первого нечеткого метода на 18% быстрее по сравнению с детектором Канни и на 2 % по отношению ко второму нечеткому методу. Однако при визуальной оценке установлено, что второй нечеткий метод лучше определяет границы объектов.
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- 2022
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20. Finite-time lag projective synchronization of delayed fractional-order quaternion-valued neural networks with parameter uncertainties
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Weiying Shang, Weiwei Zhang, Hai Zhang, Hongmei Zhang, Jinde Cao, and Fawaz E. Alsaadi
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quaternion-valued neural networks ,finite-time lag projective synchronization ,parameter uncertainties ,Analysis ,QA299.6-433 - Abstract
This paper discusses a class issue of finite-time lag projective synchronization (FTLPS) of delayed fractional-order quaternion-valued neural networks (FOQVNNs) with parameter uncertainties, which is solved by a non-decomposition method. Firstly, a new delayed FOQVNNs model with uncertain parameters is designed. Secondly, two types of feedback controller and adaptive controller without sign functions are designed in the quaternion domain. Based on the Lyapunov analysis method, the non-decomposition method is applied to replace the decomposition method that requires complex calculations, combined with some quaternion inequality techniques, to accurately estimate the settling time of FTLPS. Finally, the correctness of the obtained theoretical results is testified by a numerical simulation example.
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- 2023
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21. Dynamics of information-awareness-epidemic-activity coevolution in multiplex networks
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Jie Chen, Maobin Hu, and Jinde Cao
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Physics ,QC1-999 - Abstract
Epidemic spreading and awareness diffusion are typically driven by information exchange and physical contact generated by activities, respectively, evolving in a synergistic manner. In response to this reality, we propose a dynamic model of information-awareness-epidemic-activity coevolution on a four-layer network. Our findings reveal the presence of an optimal coupling between information contact preference and activity contact preference, which efficiently suppresses epidemic spreading. Specifically, the disease-related information should be targeted towards individuals who engage in more activities, enhancing their awareness and resistance to infection. Examining the epidemic situation, we observe that the epidemic threshold can be moderately increased with higher information levels but significantly decreased with increased activity frequency. Quantitatively, we establish that the epidemic threshold is strictly inversely proportional to the activity frequency. By integrating the microscopic Markov chain approach with the mean-field method, we provide theoretical insights into the system's state size and epidemic threshold. We derive an explicit expression for the critical combination of information level and activity frequency required to prevent epidemic outbreaks. These results are consistently supported by extensive Monte Carlo simulations on both heterogeneous scale-free multiplex networks and homogeneous Erdős-Rényi multiplex networks. This research emphasizes the crucial importance of reducing physical contact through activities as a key preventive measure against epidemics, complementing the focus on information dissemination to raise awareness.
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- 2023
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22. Synchronizations of fuzzy cellular neural networks with proportional time-delay
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Ankit Kumar, Subir Das, Vijay K. Yadav, Rajeev, Jinde Cao, and Chuangxia Huang
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finite-time synchronization ,fixed-time synchronization ,fuzzy cellular neural network ,interaction term ,proportional delay term ,Mathematics ,QA1-939 - Abstract
In this article, finite-time and fixed-time synchronizations (FFTS) of fuzzy cellular neural networks (FCNNs) with interaction and proportional delay terms have been investigated. The synchronizations of FCNNs are achieved with the help of p-norm based on the inequalities defined in Lemmas 2.1 and 2.2. The analysis of the method with some useful criteria is also used during the study of FFTS. Under the Lyapunov stability theory, FFTS of fuzzy-based CNNs with interaction and proportional delay terms can be achieved using controllers. Moreover, the upper bound of the settling time of FFTS is obtained. In view of settling points, the theoretical results on the considered neural network models of this article are more general as compared to the fixed time synchronization (FTS). The effectiveness and reliability of the theoretical results are shown through two numerical examples for different particular cases.
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- 2021
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23. Discrete Superior Hyperbolicity in Chaotic Maps
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Fawaz Alsaadi, Jinde Cao, A. K. Malik, and Ashish Ashish
- Subjects
chaos ,hyperbolicity ,bifurcation plot ,chaotic maps ,Electronic computers. Computer science ,QA75.5-76.95 ,Applied mathematics. Quantitative methods ,T57-57.97 - Abstract
In the last few decades, the dynamics of one-dimensional chaotic maps have gained the tremendous attention of scientists and scholars due to their remarkable properties such as period-doubling, chaotic evolution, Lyapunov exponent, etc. The term hyperbolicity, another important property of chaotic maps is used to examine the regular and irregular behavior of the dynamical systems. In this article, we deal with the hyperbolicity and stabilization of fixed states using a superior two-step feedback system. Due to the superiority in the chaotic evolution of one-dimensional maps in the superior system we are encouraged to examine the hyperbolicity and stabilization in chaotic maps. The hyperbolic notion, hyperbolicity in periodic states of prime order, stabilization, and the hyperbolic set of the chaotic maps are studied. The numerical, as well as experimental simulations, are carried out, followed by theorems, examples, remarks, functional plots, and bifurcation diagrams.
- Published
- 2021
- Full Text
- View/download PDF
24. Multi-Modal Fake News Detection via Bridging the Gap between Modals
- Author
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Peng Liu, Wenhua Qian, Dan Xu, Bingling Ren, and Jinde Cao
- Subjects
multi-modal ,fake news detection ,caption-based ,transformer ,Science ,Astrophysics ,QB460-466 ,Physics ,QC1-999 - Abstract
Multi-modal fake news detection aims to identify fake information through text and corresponding images. The current methods purely combine images and text scenarios by a vanilla attention module but there exists a semantic gap between different scenarios. To address this issue, we introduce an image caption-based method to enhance the model’s ability to capture semantic information from images. Formally, we integrate image description information into the text to bridge the semantic gap between text and images. Moreover, to optimize image utilization and enhance the semantic interaction between images and text, we combine global and object features from the images for the final representation. Finally, we leverage a transformer to fuse the above multi-modal content. We carried out extensive experiments on two publicly available datasets, and the results show that our proposed method significantly improves performance compared to other existing methods.
- Published
- 2023
- Full Text
- View/download PDF
25. Enhancing the Mathematical Theory of Nabla Tempered Fractional Calculus: Several Useful Equations
- Author
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Yiheng Wei, Linlin Zhao, Xuan Zhao, and Jinde Cao
- Subjects
nabla discrete time ,tempered fractional calculus ,nabla Taylor series ,nabla Laplace transform ,Thermodynamics ,QC310.15-319 ,Mathematics ,QA1-939 ,Analysis ,QA299.6-433 - Abstract
Although many applications of fractional calculus have been reported in literature, modeling the physical world using this technique is still a challenge. One of the main difficulties in solving this problem is that the long memory property is necessary, whereas the infinite memory is undesirable. To address this challenge, a new type of nabla fractional calculus with a weight function is formulated, which combines the benefits of nabla fractional calculus and its tempered counterpart, making it highly valuable for modeling practical systems. However, many properties of this calculus are still unclear and need to be discovered. Therefore, this paper gives particular emphasis to the topic, developing some remarkable properties, i.e., the equivalence relation, the nabla Taylor formula, and the nabla Laplace transform of such nabla tempered fractional calculus. All the developed properties greatly enrich the mathematical theory of nabla tempered fractional calculus and provide high value and potential for further applications.
- Published
- 2023
- Full Text
- View/download PDF
26. A Brief Survey of Recent Advances and Methodologies for the Security Control of Complex Cyber–Physical Networks
- Author
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Ying Wan and Jinde Cao
- Subjects
complex cyber–physical networks ,secure control ,hybrid attack ,denial-of-service (DoS) attack ,false data injection (FDI) attack ,proactive defense ,Chemical technology ,TP1-1185 - Abstract
Complex cyber–physical networks combine the prominent features of complex networks and cyber–physical systems (CPSs), and the interconnections between the cyber layer and physical layer usually pose significant impacts on its normal operation. Many vital infrastructures, such as electrical power grids, can be effectively modeled as complex cyber–physical networks. Given the growing importance of complex cyber–physical networks, the issue of their cybersecurity has become a significant concern in both industry and academic fields. This survey is focused on some recent developments and methodologies for secure control of complex cyber–physical networks. Besides the single type of cyberattack, hybrid cyberattacks are also surveyed. The examination encompasses both cyber-only hybrid attacks and coordinated cyber–physical attacks that leverage the strengths of both physical and cyber attacks. Then, special focus will be paid to proactive secure control. Reviewing existing defense strategies from topology and control perspectives aims to proactively enhance security. The topological design allows the defender to resist potential attacks in advance, while the reconstruction process can aid in reasonable and practical recovery from unavoidable attacks. In addition, the defense can adopt active switching-based control and moving target defense strategies to reduce stealthiness, increase the cost of attacks, and limit the attack impacts. Finally, conclusions are drawn and some potential research topics are suggested.
- Published
- 2023
- Full Text
- View/download PDF
27. Finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks via non-reduced order method
- Author
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Ruoyu Wei, Jinde Cao, Wenhua Qian, Changfeng Xue, and Xiaoshuai Ding
- Subjects
cohen-grossberg neural networks ,inertial term ,mixed time delays ,finite-time (fixed-time) stabilization ,Mathematics ,QA1-939 - Abstract
In this paper, we focus on the finite-time and fixed-time stabilization of inertial memristive Cohen-Grossberg neural networks. To cope with the effect caused by inertial (second-order) term, most of the previous literature use the variable translation to reduce the order. Different from that, by directly designing a Lyapunov functional and feedback controller, a novel non-reduced order method is proposed in this paper to solve the finite-time (fixed-time) stabilization problem of inertial memristive Cohen-Grossberg neural networks. Two kinds of time delays are considered in our network model, novel criteria are then derived for both cases. Lastly, numerical examples are given to verify the validity of the theoretical results.
- Published
- 2021
- Full Text
- View/download PDF
28. Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition
- Author
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Sekar Elango, Ayyadurai Tamilselvan, R. Vadivel, Nallappan Gunasekaran, Haitao Zhu, Jinde Cao, and Xiaodi Li
- Subjects
Parabolic delay differential equations ,Singular perturbation problem ,Integral boundary condition ,Shishkin mesh ,Finite difference scheme ,Boundary layers ,Mathematics ,QA1-939 - Abstract
Abstract This paper investigates singularly perturbed parabolic partial differential equations with delay in space, and the right end plane is an integral boundary condition on a rectangular domain. A small parameter is multiplied in the higher order derivative, which gives boundary layers, and due to the delay term, one more layer occurs on the rectangle domain. A numerical method comprising the standard finite difference scheme on a rectangular piecewise uniform mesh (Shishkin mesh) of N r × N t $N_{r} \times N_{t}$ elements condensing in the boundary layers is suggested, and it is proved to be parameter-uniform. Also, the order of convergence is proved to be almost two in space variable and almost one in time variable. Numerical examples are proposed to validate the theory.
- Published
- 2021
- Full Text
- View/download PDF
29. Asymptotic behavior of Clifford-valued dynamic systems with D-operator on time scales
- Author
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Chaouki Aouiti, Imen Ben Gharbia, Jinde Cao, and Xiaodi Li
- Subjects
Clifford-valued ,Neutral type ,High-order neural networks ,Time scales ,Global exponential stability ,Pseudo almost periodic function ,Mathematics ,QA1-939 - Abstract
Abstract In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are taken into account. As an extension of the real-valued neural network, the Clifford-valued neural network, which includes a familiar complex-valued neural network and a quaternion-valued neural network as special cases, has been an active research field recently. By utilizing this novel method, which incorporates the differential inequality techniques and the fixed point theorem and time-scale theory of computation, we derive a few sufficient conditions to ensure the existence, uniqueness, and exponential stability of the pseudo almost periodic (PAP) solution of the considered model. The results in this paper are new, even if time scale T = R $\mathbb{T}=\mathbb{R}$ or T = Z $\mathbb{T}=\mathbb{Z}$ , and complementary to the previously existing works. Furthermore, an example and its numerical simulations are included to demonstrate the validity and advantage of the obtained results.
- Published
- 2021
- Full Text
- View/download PDF
30. Positive almost periodicity on SICNNs incorporating mixed delays and D operator
- Author
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Chuangxia Huang, Bingwen Liu, Hedi Yang, and Jinde Cao
- Subjects
positive almost periodic solution ,stability ,shunting inhibitory cellular neural networks ,D operator ,mixed delay ,Analysis ,QA299.6-433 - Abstract
This article involves a kind of shunting inhibitory cellular neural networks incorporating D operator and mixed delays. First of all, we demonstrate that, under appropriate external input conditions, some positive solutions of the addressed system exist globally. Secondly, with the help of the differential inequality techniques and exploiting Lyapunov functional approach, some criteria are established to evidence the globally exponential stability on the positive almost periodic solutions. Eventually, a numerical case is provided to test and verify the correctness and reliability of the proposed findings.
- Published
- 2022
- Full Text
- View/download PDF
31. How to empower Grünwald–Letnikov fractional difference equations with available initial condition?
- Author
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Yiheng Wei, Jinde Cao, Chuang Li, and Yangquan Chen
- Subjects
fractional calculus ,independence ,initial condition ,Grünwald–Letnikov definition ,dynamic properties ,Analysis ,QA299.6-433 - Abstract
In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution x(k) of equation aG∇kαx(k) = f(x(k)), k > a + 1, cannot be calculated with initial condition x(a). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp.
- Published
- 2022
- Full Text
- View/download PDF
32. Hamilton-connectedness and Hamilton-laceability of planar geometric graphs with applications
- Author
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Suliman Khan, Sakander Hayat, Asad Khan, Muhammad Yasir Hayat Malik, and Jinde Cao
- Subjects
graph ,hamiltonian path ,hamiltonian cycle ,hamilton-connected graph ,detour index ,np-complete problems ,platonic solids ,convex polytopes ,Mathematics ,QA1-939 - Abstract
In this paper, we have used two different proof techniques to show the Hamilton-connectedness of graphs. By using the vertex connectivity and Hamiltoniancity of graphs, we construct an infinite family of Hamilton-connected convex polytope line graphs whose underlying family of convex polytopes is not Hamilton-connected. By definition, we constructed two more infinite families of Hamilton-connected convex polytopes. As a by-product of our results, we compute exact values of the detour index of the families of Hamilton-connected convex polytopes. Finally, we classify the Platonic solids according to their Hamilton-connectedness and Hamilton-laceability properties.
- Published
- 2021
- Full Text
- View/download PDF
33. A Razumikhin approach to stability and synchronization criteria for fractional order time delayed gene regulatory networks
- Author
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Pratap Anbalagan, Evren Hincal, Raja Ramachandran, Dumitru Baleanu, Jinde Cao, and Michal Niezabitowski
- Subjects
gene regulatory networks ,fractional-order ,existence and stability ,synchronization ,linear feedback control ,adaptive feedback control ,Mathematics ,QA1-939 - Abstract
This manuscript is concerned with the stability and synchronization for fractional-order delayed gene regulatory networks (FODGRNs) via Razumikhin approach. First of all, the existence of FODGRNs are established by using homeomorphism theory, 2-norm based on the algebraic method and Cauchy Schwartz inequality. The uniqueness of this work among the existing stability results are, the global Mittag-Leffler stability of FODGRNs is explored based on the fractional-order Lyapunov Razumikhin approach. In the meanwhile, two different controllers such as linear feedback and adaptive feedback control, are designed respectively. With the assistance of fractional Razumikhin theorem and our designed controllers, we have established the global Mittag-Leffler synchronization and adaptive synchronization for addressing master-slave systems. Finally, three numerical cases are given to justify the applicability of our stability and synchronization results.
- Published
- 2021
- Full Text
- View/download PDF
34. On the zero forcing number and propagation time of oriented graphs
- Author
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Sakander Hayat, Hafiz Muhammad Afzal Siddiqui, Muhammad Imran, Hafiz Muhammad Ikhlaq, and Jinde Cao
- Subjects
graph coloring ,zero forcing process ,propagation time ,oriented graphs ,graph applications ,Mathematics ,QA1-939 - Abstract
Zero forcing is a process of coloring in a graph in time steps known as propagation time. These graph-theoretic parameters have diverse applications in computer science, electrical engineering and mathematics itself. The problem of evaluating these parameters for a network is known to be NP-hard. Therefore, it is interesting to study these parameters for special families of networks. Perila et al. (2017) studied properties of these parameters for some basic oriented graph families such as cycles, stars and caterpillar networks. In this paper, we extend their study to more non-trivial structures such as oriented wheel graphs, fan graphs, friendship graphs, helm graphs and generalized comb graphs. We also investigate the change in propagation time when the orientation of one edge is flipped.
- Published
- 2021
- Full Text
- View/download PDF
35. Nonnegative periodicity on high-order proportional delayed cellular neural networks involving D operator
- Author
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Xiaojin Guo, Chuangxia Huang, and Jinde Cao
- Subjects
high-order cellular neural network ,proportional delay ,nonnegative periodic solution ,global exponential stability ,d operator ,Mathematics ,QA1-939 - Abstract
This paper aims to deal with the dynamic behaviors of nonnegative periodic solutions for one kind of high-order proportional delayed cellular neural networks involving D operator. By utilizing Lyapunov functional approach, combined with some dynamic inequalities, we establish a new assertion to guarantee the existence and global exponential stability of nonnegative periodic solutions for the addressed networks. The obtained results supplement and improve some existing ones. In addition, the correctness of the analytical results are verified by numerical simulations.
- Published
- 2021
- Full Text
- View/download PDF
36. Neuro-swarms intelligent computing using Gudermannian kernel for solving a class of second order Lane-Emden singular nonlinear model
- Author
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Zulqurnain Sabir, Muhammad Asif Zahoor Raja, Adnène Arbi, Gilder Cieza Altamirano, and Jinde Cao
- Subjects
lane-emden singular system ,gudermannian neural networks ,sequential quadratic scheme ,gudermannian kernel ,numerical results ,particle swarm optimization ,Mathematics ,QA1-939 - Abstract
The present work is to design a novel Neuro swarm computing standards using artificial intelligence scheme to exploit the Gudermannian neural networks (GNN)accomplished with global and local search ability of particle swarm optimization (PSO) and sequential quadratic programming scheme (SQPS), called as GNN-PSO-SQPS to solve a class of the second order Lane-Emden singular nonlinear model (SO-LES-NM). The suggested intelligent computing solver GNN-PSO-SQPS using the Gudermannian kernel are unified with the configuration of the hidden layers of GNN of differential operators for solving the SO-LES-NM. An error based fitness function (FF) applying the differential form of the differential model and corresponding boundary conditions. The FF is optimized together with the combined heuristics of PSO-SQPS. Three problems of the SO-LES-NM are solved to validate the correctness, effectiveness and competence of the designed GNN-PSO-SQPS. The performance of the GNN-PSO-SQPS through statistical operators is tested to check the constancy, convergence and precision.
- Published
- 2021
- Full Text
- View/download PDF
37. Delay-coupled fractional order complex Cohen-Grossberg neural networks under parameter uncertainty: Synchronization stability criteria
- Author
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Pratap Anbalagan, Evren Hincal, Raja Ramachandran, Dumitru Baleanu, Jinde Cao, Chuangxia Huang, and Michal Niezabitowski
- Subjects
synchronization stability ,fractional order ,complex coupled cohen-grossberg neural networks ,kronecker product ,linear coupling delay ,Mathematics ,QA1-939 - Abstract
This paper inspects the issues of synchronization stability and robust synchronization stability for fractional order coupled complex interconnected Cohen-Grossberg neural networks under linear coupling delays. For investigation of synchronization stability results, the comparison theorem for multiple delayed fractional order linear system is derived at first. Then, by means of given fractional comparison principle, some inequality methods, Kronecker product technique and classical Lyapunov-functional, several asymptotical synchronization stability criteria are addressed in the voice of linear matrix inequality (LMI) for the proposed model. Moreover, when parameter uncertainty exists, we also the investigate on the robust synchronization stability criteria for complex structure on linear coupling delayed Cohen-Grossberg type neural networks. At last, the validity of the proposed analytical results are performed by two computer simulations.
- Published
- 2021
- Full Text
- View/download PDF
38. Quantifying some distance topological properties of the non-zero component graph
- Author
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Fawaz E. Alsaadi, Faisal Ali, Imran Khalid, Masood Ur Rehman, Muhammad Salman, Madini Obad Alassafi, and Jinde Cao
- Subjects
distance ,distance-based topological descriptors ,non-zero component graph ,Mathematics ,QA1-939 - Abstract
Several bioactivities of chemical compounds in a molecular graph can be expected by using many topological descriptors. A topological descriptor is a numeric quantity which quantify the topology of a graph. By defining the metric on a graph related with a vector space, we consider this graph in the context of few topological descriptors, and quantify the Wiener index, hyper Wiener index, Reciprocal complimentary Wiener index, Schultz molecular topological index and Harary index. We also provide the graphical comparison of our results to describe the relationship and dependence of these descriptors on the involved parameters.
- Published
- 2021
- Full Text
- View/download PDF
39. Exponential Synchronization of Partially Coupled Heterogeneous Networks With Time-Delays and Heterogeneous Impulsess
- Author
-
Guizhen Feng, Jinde Cao, Jian Ding, and Yishu Wang
- Subjects
Exponential synchronization ,heterogeneous networks ,partially coupled ,comparison principle ,impulse ,Electrical engineering. Electronics. Nuclear engineering ,TK1-9971 - Abstract
This work focuses on exponential synchronization for a class of partially coupled heterogeneous networks with time-delays and heterogeneous impulses. The synchronization targets are selected as the common equilibrium solution and the average trajectory, respectively. Some synchronization criteria are deduced by using Lyapunov function and comparison principle.
- Published
- 2021
- Full Text
- View/download PDF
40. Correction: Song et al. New Results on Robust Synchronization for Memristive Neural Networks with Fractional Derivatives via Linear Matrix Inequality. Fractal Fract. 2022, 6, 585
- Author
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Chao Song, Jinde Cao, and Mahmoud Abdel-Aty
- Subjects
n/a ,Thermodynamics ,QC310.15-319 ,Mathematics ,QA1-939 ,Analysis ,QA299.6-433 - Abstract
In the original publication, there were two mistakes in Figure 1 and Figure 2, as published [...]
- Published
- 2022
- Full Text
- View/download PDF
41. An Augmented Model of Rutting Data Based on Radial Basis Neural Network
- Author
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Zhuoxuan Li, Meng Tao, Jinde Cao, Xinli Shi, Tao Ma, and Wei Huang
- Subjects
rutting depth ,data augmentation model ,RIOHTrack ,radial basis function neural network ,feature engineering ,Mathematics ,QA1-939 - Abstract
The rutting depth is an important index to evaluate the damage degree of the pavement. Therefore, establishing an accurate rutting depth prediction model can guide pavement design and provide the necessary basis for pavement maintenance. However, the sample size of pavement rutting depth data is small, and the sampling is not standardized, which makes it hard to establish a prediction model with high accuracy. Based on the data of RIOHTrack’s asphalt pavement structure, this study builds a reliable data-augmented model. In this paper, different asphalt rutting data augmented models based on Gaussian radial basis neural networks are constructed with the temperature and loading of asphalt pavements as the main features. Experimental results show that the method outperforms classical machine learning methods in data augmentation, with an average root mean square error of 3.95 and an average R-square of 0.957. Finally, the augmented data of rutting depth is constructed for training, and multiple neural network models are used for prediction. Compared with unaugmented data, the prediction accuracy is increased by 50%.
- Published
- 2022
- Full Text
- View/download PDF
42. Robust synchronization in finite time for fractional-order hybrid coupling discontinuous complex dynamic networks with nonlinear growth
- Author
-
You Jia, Huaiqin Wu, and Jinde Cao
- Subjects
Complex dynamical networks ,Robust synchronization ,Synchronization in finite time ,Hybrid coupling ,Discontinuous nodes ,Fractional calculus ,Engineering (General). Civil engineering (General) ,TA1-2040 - Abstract
In this paper, the global robust synchronization and synchronization in finite time are considered for fractional-order hybrid coupling complex dynamical networks (CDNs), where the growth of dynamic nodes is discontinuous, and subjected to a quadratic polynomial. Firstly, a convergence principle in finite time is developed for fractional-order nonlinear systems with discontinuous right-hand side. Secondly, a suitable discontinuous controller without the terms of time delays is designed, and the global robust synchronization condition is addressed in the terms of linear matrix inequalities (LMIs) by applying Lyapunov functional approach, inequality analysis technique, and Clarke’s non-smooth analysis method. In addition, the global robust synchronization goal in finite time is achieved by utilizing the developed convergence principle. Moreover, the upper bound of the settling time for the global robust synchronization in finite time is explicitly evaluated. Finally, the feasibility of the proposed design scheme and the validity of theoretical results are verified by two numerical simulation examples.
- Published
- 2020
- Full Text
- View/download PDF
43. Finite-time stabilization for fractional-order inertial neural networks with time varying delays
- Author
-
Chaouki Aouiti, Jinde Cao, Hediene Jallouli, and Chuangxia Huang
- Subjects
inertial neural networks ,finite-time stabilization ,fractional-order system ,Caputo fractional derivative and integral ,Analysis ,QA299.6-433 - Abstract
This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results.
- Published
- 2022
- Full Text
- View/download PDF
44. Spatiotemporal Evolution Characteristics of Time-Delay Ecological Competition Systems with Food-Limited and Diffusion
- Author
-
Feilong Wang, Min Xiao, Zhengxin Wang, Jing Zhao, Gong Chen, and Jinde Cao
- Subjects
Electronic computers. Computer science ,QA75.5-76.95 - Abstract
In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis.
- Published
- 2022
- Full Text
- View/download PDF
45. Some spectral sufficient conditions for a graph being pancyclic
- Author
-
Huan Xu, Tao Yu, Fawaz E. Alsaadi, Madini Obad Alassafi, Guidong Yu, and Jinde Cao
- Subjects
pancyclic graph ,edge number ,spectral radius ,signless laplacian spectral radius ,Mathematics ,QA1-939 - Abstract
Let $G(V,E)$ be a simple connected graph of order $n$. A graph of order $n$ is called pancyclic if it contains all the cycles $C_k$ for $k\in \{3,4,\cdot\cdot\cdot,n\}$. In this paper, some new spectral sufficient conditions for the graph to be pancyclic are established in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.
- Published
- 2020
- Full Text
- View/download PDF
46. Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients
- Author
-
Ruoyu Wei, Jinde Cao, and Jurgen Kurths
- Subjects
quaternion ,time-varying coefficients ,bidirectional associative memory neural networks (bamnns) ,adaptive control ,fixed-time stabilization ,Mathematics ,QA1-939 - Abstract
In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixedtime control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results.
- Published
- 2020
- Full Text
- View/download PDF
47. On the construction, properties and Hausdorff dimension of random Cantor one pth set
- Author
-
Sudesh Kumari, Renu Chugh, Jinde Cao, and Chuangxia Huang
- Subjects
nonlinear dynamics ,random construction ,random cantor one pth set ,hausdorff dimension ,martingale ,probability ,Mathematics ,QA1-939 - Abstract
In 1883, German Mathematician George Cantor introduced Cantor ternary set which is a self-similar fractal. K. J. Falconer (1990) defined random Cantor set with statistical self-similarity. The purpose of this paper is to introduce generalized random Cantor sets (one 5th, one 7th and in general one pth). Some properties and results of random Cantor one pth set have also been obtained. We compute Hausdorff dimension of random Cantor one pth sets and show that Hausdorff dimension of these random Cantor sets is less than that of Hausdorff dimension of Cantor one pth sets, calculated by Ashish et al. (2013).
- Published
- 2020
- Full Text
- View/download PDF
48. Asymptotic behavior for a class of population dynamics
- Author
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Chuangxia Huang, Luanshan Yang, and Jinde Cao
- Subjects
population dynamics ,time-varying delay ,asymptotic behavior ,bernfeld-haddock conjecture ,Mathematics ,QA1-939 - Abstract
This paper investigates the asymptotic behavior for a class of n-dimensional population dynamics systems described by delay differential equations. With the help of technique of differential inequality, we show that each solution of the addressed systems tends to a constant vector as t → ∞, which includes many generalizations of Bernfeld-Haddock conjecture. By the way, our results extend some existing literatures.
- Published
- 2020
- Full Text
- View/download PDF
49. Finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks
- Author
-
A. Pratap, R. Raja, Jinde Cao, J. Alzabut, and Chuangxia Huang
- Subjects
Discontinuous fractional-order neural networks ,Coupled systems ,Finite time synchronization ,Mathematics ,QA1-939 - Abstract
Abstract In this research work, the finite-time synchronization and adaptive finite-time synchronization criterion of graph theory perspective fractional-order coupled discontinuous neural networks (FCDNNs) are investigated under two different control strategies. By utilizing differential inclusion theory, Filippov framework, suitable Lyapunov functional, and graph theory approach, several sufficient criteria based on discontinuous state feedback control protocol and discontinuous adaptive feedback control protocol are established for ensuring the finite-time synchronization and adaptive finite-time synchronization of FCDNNs. Finally, two numerical cases illustrate the efficiency of the proposed finite-time synchronization results.
- Published
- 2020
- Full Text
- View/download PDF
50. Fixed time synchronization of delayed quaternion-valued memristor-based neural networks
- Author
-
Dingyuan Chen, Weiwei Zhang, Jinde Cao, and Chuangxia Huang
- Subjects
Fixed time synchronization ,Lyapunov function ,Quaternion ,Time varying delays ,Memristor-based neural networks ,Mathematics ,QA1-939 - Abstract
Abstract This paper investigates the fixed time synchronization issue for a class of quaternion-valued memristor-based neural networks (QVMNN) at the presence of time varying delays. Differential inclusion and fixed time stability theory are used, and new synchronization conditions are formulated to achieve the synchronization of delayed QVMNN within a fixed time based on a Lyapunov function and a suitable controller. The feasibility of the proposed method is shown through numerical simulations.
- Published
- 2020
- Full Text
- View/download PDF
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